Transverse vibration of thick polygonal plates using analytically integrated trapezoidal Fourier p-element

Computers and Structures

Volumn 82, Issue 2-3, 2004, Pages 109-119

  Leung, A Y T ^a   Zhu, B ^a  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Fourier; P element; Thick plates; Trapezoid; Vibration

Indexed keywords

BENDING (DEFORMATION); BOUNDARY CONDITIONS; COMPUTATIONAL METHODS; DEGREES OF FREEDOM (MECHANICS); FINITE ELEMENT METHOD; FUNCTIONS; INTEGRATION; NATURAL FREQUENCIES; POLYNOMIALS; VIBRATIONS (MECHANICAL);

THICK PLATES; TRAPEZOIDS;

PLATES (STRUCTURAL COMPONENTS);

EID: 0346094020     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruc.2003.10.002     Document Type: Article

References (22)

1. Bardell N.S. Free vibration analysis of a flat plate using the hierarchical finite element method. J. Sound Vib. 151(2):1991;263-289.
2. Bardell N.S. The free vibration of skew plates using the hierarchical finite element method. Comput. Struct. 45(5-6):1992;841-874.
3. Houmat A. An alternative hierarchical finite element formulation applied to plate vibrations. J. Sound Vib. 206(2):1997;201-215.
4. Beslin O., Nicolas J. Hierarchical functions set for predicting very high order plate bending modes with any boundary conditions. J. Sound Vib. 202(5):1997;633-655.
5. Houmat A. A sector Fourier. p -element applied to free vibration analysis of sectorial plates J. Sound Vib. 243(2):2001;269-282.
6. Leung A.Y.T., Chan J.K.W. Fourier. p -element for the analysis of beams and plates J. Sound Vib. 212(1):1998;179-185.
7. Houmat A. A sector Fourier. p -element for free vibration analysis of sectorial membranes Comput. Struct. 79(12):2001;1147-1152.
8. Bogner FK, Fox RL, Schmit LA. The generation of inter-element compatible stiffness and mass matrices by the use of interpolation formulas. In: Proceedings of the 1st Conference on Matrix Methods in Structural Mechanics, Ohio, USA, 1965. p. 397-443.
9. Zienkiewicz O.C., Taylor R.L. The finite element method. 4th ed. 1989;McGraw-Hill, New York.
10. Cote A., Charron F. On the selection of p-version shape functions for plate vibration problems. Comput. Struct. 79(1):2001;119-130.
11. Ribeiro P. A hierarchical finite element for geometrically non-linear vibration of doubly curved moderately thick isotropic shallow shells. Int. J. Numer. Methods Eng. 56(5):2003;715-738.
12. Leung AYT, Zhu B, Zheng JJ, Yang H. Analytic trapezoidal Fourier p -element for vibrating plane problems. J Sound Vib, in press ( doi:10.1016/S022-460X(03)00263-3 ).
13. Mindlin R.D. Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates. J. Appl. Mech. - Trans. ASME. 18:1951;31-38.
14. Wang C.M., Lim G.T., Reddy J.N., Lee K.H. Relationships between bending solutions of Reissner and Mindlin plate theories. Eng. Struct. 23(7):2001;838-849.
15. Wang C.M., Reddy J.N., Lee K.H. Shear deformable beams and plates. 2000;Elsevier, Oxford.
16. Liew K.M., Xiang Y., Kitipornchai S. Transverse vibration of thick rectangular plates - I. Comprehensive sets of boundary conditions. Comput. Struct. 49(1):1993;1-29.
17. Rock T., Hinton E. Free vibration and transient response of thick and thin plates using the finite element methods. Earthquake Eng. Struct. 3:1974;51-63.
18. McGee O.G., Butalia T.S. Natural vibrations of shear deformable cantilevered skew thick plates. J. Sound Vib. 176(3):1994;351-376.
19. Liew K.M., Xiang Y., Kitipornchai S., Wang C.M. Vibration of thick skew plates based on Mindlin shear deformation plate theory. J. Sound Vib. 168(1):1993;36-69.
20. Kitipornchai S., Xiang Y., Liew K.M., Lim M.K. A global approach for vibration of thick trapezoidal plates. Comput. Struct. 53(1):1994;83-92.
21. Kitipornchai S., Liew K.M., Xiang Y., Wang C.M. Free flexural vibration of triangular Mindlin plates. Int. J. Mech. Sci. 35(2):1993;89-102.
22. Kardestuncer H. Finite element handbook. 1987;McGraw-Hill, New York.